Low-ripple adjustable DC stabilized power supply main circuit parameter stability domain determination method based on Buck-Boost inverter circuit

Abstract

The invention discloses a method for determining a parameter stability domain of a main circuit of a low-ripple adjustable direct-current stabilized power supply based on a Buck-Boost inverter circuit. The method comprises the following steps: establishing a mathematical model of a direct-current stabilized power supply main circuit; establishing a state differential equation of the three-phase Buck-Boost inverter circuit by taking a capacitor voltage and an inductor current in the inverter circuit as state variables and taking a PWM (Pulse-Width Modulation) direct-current voltage and an output current of the inverter circuit as input and output variables of the inverter circuit; establishing an equivalent mathematical model between the input current and the input voltage of the three-phase uncontrollable rectification circuit; obtaining a discrete iterative mapping model of the DC stabilized power supply according to a mathematical model of PWM modulation DC voltage, a state differential equation of the three-phase Buck-Boost inverter circuit and an equivalent mathematical model of the three-phase uncontrollable rectification circuit; according to the obtained discrete iteration mapping model, the value range of the main circuit parameters of the direct-current stabilized power supply during stable operation is obtained through numerical simulation, and stable operation of the direct-current stabilized power supply is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronic system stability analysis, and particularly relates to a method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit. Background Art

[0002] The low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit is a new type of DC regulated power supply topology with a simple structure. This power supply structure consists of a three-phase PWM rectifier circuit, a three-phase Buck-Boost inverter circuit, and a three-phase uncontrolled rectifier circuit. However, since this DC regulated power supply is a variable-structure strong nonlinear system, bifurcation and chaos phenomena will occur under certain conditions, leading to unstable operation. Therefore, it is of great significance to carry out stability research on this DC regulated power supply.

[0003] Currently, relevant research has been carried out on the stability analysis of Buck-Boost converters, especially DC regulated power supplies based on Buck-Boost converters. Among them, the literature "Research on the Nonlinear Characteristics of Buck-Boost Converters Based on Pulse Input Voltage" (Journal of System Simulation, 2017, 29(5): 1021-1027) studied the system stability of Buck-Boost converters under the action of equal-amplitude and equal-width pulse voltages; while the patent "Method for Determining the Stability Region of the Main Circuit Parameters of a DC Chopper Power Supply Based on a Buck-Boost Inverter" (Chinese Patent: CN118573020B) carried out stability research on a DC chopper power supply composed of a three-phase Buck-Boost inverter circuit and a three-phase uncontrolled rectifier circuit under the action of a constant DC voltage, and determined the stability region of its main circuit parameters. However, for the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit studied in this application, since the output of its three-phase PWM rectifier circuit is a PWM-modulated DC voltage, which is a pulse voltage sequence with variable pulse amplitude and variable duty cycle changing according to a certain law. When this variable-amplitude and variable-duty cycle pulse voltage is used as the input voltage of the three-phase Buck-Boost inverter circuit, the above-mentioned mathematical modeling and analysis methods for system stability are no longer applicable. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a method for mathematical modeling of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit and for determining the stability region of its main circuit parameters. Through the present invention, the range of the stability region of the main circuit parameters of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit can be determined.

[0005] The technical solution of the present invention to solve the above technical problems is: a method for determining the stable region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit, including the following steps:

[0006] (1) Establish a mathematical model of the PWM-modulated DC voltage output by a three-phase PWM rectifier circuit; specifically: the three-phase PWM rectifier circuit adopts a space vector modulation strategy without zero vectors, and the obtained PWM-modulated DC voltage is a pulse voltage sequence in which the pulse voltage amplitude and duty cycle change with time. The mathematical model of the pulse voltage sequence is:

[0007] The high and low level values of the i-th pulse voltage are:

[0008] (1);

[0009] Where: U Hi is the high-level amplitude of the i-th (i = 1, 2, 3...) pulse voltage, U L is the low-level voltage value of the pulse voltage, V m and ω are the effective value and angular frequency of the input AC voltage of the three-phase PWM rectifier circuit respectively, t i and t i+1 are the starting moments of the i-th and (i + 1)-th pulse voltages respectively, t i ’ is the falling edge moment of the i-th pulse voltage;

[0010] The duty cycle of the i-th pulse voltage is:

[0011] (2);

[0012] (2) Establish the state differential equation of the three-phase Buck-Boost inverter circuit;

[0013] (3) Establish an equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit;

[0014] (4) According to the mathematical model obtained in step (1), the state differential equation obtained in step (2), and the equivalent mathematical model obtained in step (3), obtain the discrete iterative mapping model of the DC regulated power supply;

[0015] (5) In the range of pulse voltage amplitudes and duty cycles corresponding to the PWM-modulated DC voltage, arbitrarily select a set of pulse voltage amplitudes and duty cycles, and according to the discrete iterative mapping model obtained in step (4), obtain the value range of the main circuit parameters for the stable operation of the DC regulated power supply through numerical simulation;

[0016] (6) Change the amplitude and duty cycle of the pulse voltage successively at a certain interval, and obtain the value ranges of the main circuit parameters when the DC regulated power supply operates stably under the amplitude and duty cycle of the pulse voltage in n groups by the same method as in step (5);

[0017] (7) According to the value ranges of the main circuit parameters and their corresponding pulse voltage amplitudes and duty cycles when the DC regulated power supply operates stably under the amplitude and duty cycle of the pulse voltage in n groups obtained in step (6), use the numerical fitting method to obtain the functional relationship between the value ranges of each main circuit parameter and the pulse voltage amplitude and duty cycle;

[0018] (8) According to the functional relationship of the value ranges of each main circuit parameter obtained above and the pulse voltage amplitude and duty cycle at the input side of the Buck - Boost inverter circuit when the DC regulated power supply actually operates, obtain the value ranges of each main circuit parameter when the power supply operates stably under the amplitude and duty cycle of the pulse voltage.

[0019] Preferably, the specific steps for establishing the state differential equation of the three - phase Buck - Boost inverter circuit in step (2) are as follows:

[0020] Since the three - phase Buck - Boost inverter circuit is composed of three sets of Buck - Boost DC / DC converters with the same structure, in the following analysis, take the A - phase as an example, and the other two phases are the same;

[0021] The two power switches Q1 and Q2 in the A - phase converter are in a complementary working state. Establish the state differential equations for its two complementary working states respectively, which are:

[0022] State I: Q1 is on, Q2 is off:

[0023] (3);

[0024] State II: Q1 is off, Q2 is on:

[0025] (4);

[0026] In the formula: is the system state vector, is the input - output state vector, i L is the inductor current, u C is the capacitor voltage, U in is the pulse voltage at the input side of the converter, i o is the output current of the converter, and A1, A2, B1, and B2 are all real - valued matrices, specifically:

[0027] , ;

[0028] , .

[0029] Wherein: R on is the on-state equivalent resistance of the power switch tube, R L is the equivalent resistance of the inductor, and L and C are the inductor value and the capacitor value respectively.

[0030] Preferably, the specific steps for establishing the equivalent mathematical model between the input current and the input voltage of the three-phase uncontrolled rectifier circuit in step (3) are as follows:

[0031] The three-phase uncontrolled rectifier circuit is equivalent to being composed of a dead zone module and an adjustment gain module, and its equivalent mathematical model is:

[0032] (5);

[0033] Wherein: i o and u o are respectively the output current and the output voltage of the three-phase Buck-Boost inverter circuit, where u o =U m sinωt; u z is the limit value of the dead zone module, is the adjustment gain value, and the optimal values of u z and are obtained by numerical simulation method.

[0034] Preferably, the specific steps for obtaining the discrete iteration mapping model in step (4) are as follows:

[0035] From equations (1), (2), (3), (4) and (5), the discrete iteration mapping mathematical model of this DC regulated power supply is:

[0036] (6);

[0037] Wherein: i n+1 and u n+1 are respectively the inductor current and the capacitor voltage of the converter at (n + 1)T moment; T is the switching period of the power switch tube in the converter; α, β, e, X, Y are all intermediate variables, and are respectively: ; ; ; ; ; ; ; ; t a is the conduction time of the power switch tube Q1 within the (n + 1)-th switching period T, t bis the turn-off time of the power switch Q1 in the (n + 1)-th switching period T, i Lref is the inductor reference current, u Cref is the capacitor reference voltage, i n and u n are respectively the inductor current and capacitor voltage of the converter at nT moment.

[0038] Preferably, the specific steps of step (5) are as follows:

[0039] Step (5-1): Set system parameters, including: the equivalent resistance R L of the inductor L, the on-state equivalent resistance R on of the power switch, the switching period T, the maximum number of iterations K, the deviation value between two adjacent iteration variables , the capacitor reference voltage u Cref , and the initial value of the number of iterations n is taken as 1;

[0040] Step (5-2): Set the amplitude and duty cycle of the input pulse voltage to U H and d0 respectively;

[0041] Step (5-3): Assume that the value of the main circuit inductor in the Buck-Boost converter remains unchanged, and take its value as L. Take the capacitor C in the Buck-Boost converter as the variable parameter, take its initial value as 0, and take ΔC as the variation step size;

[0042] Step (5-4): Calculate the inductor current i n+1 and capacitor voltage u n+1 at (n + 1)T moment according to formula (6);

[0043] Step (5-5): Judge whether both and are satisfied; if so, the system is in a stable state, execute step (5-8), otherwise, execute step (5-6);

[0044] Step (5-6): Judge whether the number of iterations n is greater than K, if so, execute step (5-7); otherwise, increase the number of iterations n by 1 and return to step (5-4);

[0045] Step (5-7): Add the set step size ΔC to the capacitor value C, reset the number of iterations n to 1 and return to step (5-4);

[0046] Step (5-8): Let the corresponding capacitor value at this time be the lower limit value C min of its stable region;

[0047] Step (5 - 9): Arbitrarily select a capacitance value C within the capacitance stability range determined in steps (5 - 8) and keep it unchanged. Take the inductance L as the variable parameter, with its initial value being 0, the iteration count n being returned as 1, and ΔL as the variable step size.

[0048] Step (5 - 10): Calculate the inductor current i at time (n + 1)T according to Equation (6) n+1 and the capacitor voltage u n+1 ;

[0049] Step (5 - 11): Determine whether both and are satisfied; if so, the system is in a stable state, execute step (5 - 12), otherwise, execute step (5 - 13);

[0050] Step (5 - 12): Add the set step size ΔL to the inductance value L, return the iteration count n as 1, and return to step (5 - 10);

[0051] Step (5 - 13): Set the corresponding inductance value at this time to the upper limit value L max of its stability range.

[0052] Preferably, the specific steps of step (7) are as follows:

[0053] The functional relationship of the lower limit value of the capacitor is:

[0054] (7);

[0055] In the formula: U H is the high - level amplitude of the pulse input voltage, d0 is the duty cycle of the pulse input voltage, are all constant coefficients;

[0056] The functional relationship of the upper limit value of the inductor is:

[0057] (8);

[0058] In the formula: b0, b1, b2, b3, b4, b5 are constant coefficients.

[0059] Compared with the prior art, the technical effect of the present invention is as follows: The present invention establishes a mathematical model for the output PWM-modulated DC voltage of a three-phase PWM rectifier circuit; then, taking the capacitor voltage and inductor current in the three-phase Buck-Boost inverter circuit as state variables, and taking the output PWM-modulated DC voltage of the three-phase PWM rectifier circuit and the output current of the Buck-Boost inverter circuit as the input and output variables of the Buck-Boost inverter circuit, a state differential equation of the three-phase Buck-Boost inverter circuit is established; at the same time, an equivalent mathematical model between its input current and input voltage is established according to the structural characteristics of the three-phase uncontrolled rectifier circuit; according to the above-established mathematical model of the PWM-modulated DC voltage, the state differential equation of the three-phase Buck-Boost inverter circuit, and the equivalent mathematical model of the three-phase uncontrolled rectifier circuit, a discrete iterative mapping model of the DC regulated power supply is obtained; according to the obtained discrete iterative mapping model, the value range of the main circuit parameters when the DC regulated power supply operates stably is obtained by numerical simulation, thus laying a foundation for realizing the stable operation of the power supply and the optimal design of its main circuit parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 FIG. is the main circuit topology diagram of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit provided by the present invention.

[0061] Figure 2 FIG. is the flow chart of the method for determining the stability region of the main circuit parameters of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit provided by the present invention.

[0062] Figure 3 FIG. is the equivalent circuit structure diagram of the A-phase Buck-Boost DC / DC converter provided by the present invention.

[0063] Figure 4 FIG. is the bifurcation diagram with the capacitor as the bifurcation parameter provided by the present invention.

[0064] Figure 5 FIG. is the bifurcation diagram with the inductor as the bifurcation parameter provided by the present invention.

[0065] Figure 6 FIG. is the fitting curve graph of the functional relationship between the lower limit value of the capacitor, the pulse voltage amplitude, and the duty cycle provided by the present invention.

[0066] Figure 7 FIG. is the fitting curve graph of the functional relationship between the upper limit value of the inductor, the pulse voltage amplitude, and the duty cycle provided by the present invention.

[0067] Figure 8 FIG. is the output voltage waveform diagram corresponding to the parameters taken within the stability region of the main circuit parameters provided by the present invention.

[0068] Figure 9 The waveform diagram of the output voltage corresponding to the parameters taken outside the stable domain of the main circuit parameters provided by the present invention. Specific embodiments

[0069] The present invention will be further specifically described below in conjunction with the accompanying drawings and embodiments.

[0070] Figure 1 The main circuit topology diagram of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit provided by the present invention. This topology includes a three-phase PWM rectifier circuit, a three-phase Buck-Boost inverter circuit, and a three-phase uncontrolled rectifier circuit. Among them:

[0071] The three-phase PWM rectifier circuit is composed of 6 fully controlled power switches S1~S6. Among them, the emitters of the power switches S1, S3, and S5 are respectively connected to the collectors of S2, S4, and S6 and respectively form three groups of bridge arms. The three-phase PWM rectifier circuit is formed by the parallel connection of the three groups of bridge arms. The three-phase input alternating current is respectively connected to the midpoints of the three groups of bridge arms. The collectors of the power switches S1, S3, and S5 are connected together as the positive terminal of the DC voltage output by the PWM rectifier circuit, and the emitters of the power switches S2, S4, and S6 are connected together as the negative terminal of the DC voltage output by the PWM rectifier circuit.

[0072] The three-phase Buck-Boost inverter circuit is composed of 3 sets of Buck-Boost buck-boost circuits connected in parallel in a phase-shifted interleaved manner, including fully controlled power switch tubes Q1~Q6, inductors L1~L3, and capacitors C1~C3; among them, the on-state equivalent resistances of the power switch tubes Q1~Q6 are R on1 ~R on6 , and the equivalent resistances of the inductors are R L1 ~R L3 ; the fully controlled power switches Q1~Q6 are intended to use MOS tubes; taking the A-phase circuit as an example: the drain of the Q1 tube is connected to the positive pole of the DC power supply, the source of the Q1 tube is connected to one end of the inductor L1 and the drain of the Q2 tube, the other end of the inductor L1 is connected to the negative pole of the DC power supply, and the source of the Q2 tube is connected to one end of the capacitor C1. The other end of the capacitor C1 is connected to the other end of the inductor L1.

[0073] The three-phase uncontrolled rectifier circuit is composed of 6 rectifier diodes D1~D6 and a filter capacitor C0. Among them, the anodes of the rectifier diodes D1, D3, and D5 are respectively connected to the cathodes of the diodes D2, D4, and D6 and are respectively connected to the output ends of the three-phase Buck-Boost inverter circuit. The cathodes of the diodes D1, D3, and D5 are connected together as the positive terminal of the rectifier output, and the anodes of the diodes D2, D4, and D6 are connected together as the negative terminal of the rectifier output. The positive terminal and the negative terminal of the rectifier output are connected to the filter capacitor C0 and the load resistor R0.

[0074] Given that the circuit structures of the three phases of the three-phase Buck-Boost inverter circuit are exactly the same, and assuming that the parameters of the corresponding components in the circuit are exactly the same, the on-state equivalent resistance of each power switch tube is set as R in the following calculations on , and the equivalent resistance of the inductor is R L .

[0075] Figure 2 It is a flowchart of a method for determining the stable region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit provided by the present invention. The method includes the following steps:

[0076] Step (1): Establish a mathematical model of the PWM-modulated DC voltage output by the three-phase PWM rectifier circuit. The three-phase PWM rectifier circuit adopts a space vector modulation strategy without zero vectors. The obtained PWM-modulated DC voltage is a pulse voltage sequence whose pulse voltage amplitude and duty cycle change with time. The mathematical model of the pulse voltage sequence is as follows:

[0077] The high and low level values of the i-th pulse voltage are:

[0078] (1);

[0079] Where: U Hi is the high-level amplitude of the i-th (i = 1, 2, 3...) pulse voltage, U L is the low-level voltage value of the pulse voltage (constant), V m and ω are the effective value and angular frequency of the input AC voltage of the three-phase PWM rectifier circuit respectively, t i and t i+1 are the starting moments of the i-th and (i + 1)-th pulse voltages respectively, and t i ’ is the falling edge moment of the i-th pulse voltage.

[0080] The duty cycle of the i-th pulse voltage is:

[0081] (2);

[0082] Step (2): Establish the state differential equation of the three-phase Buck-Boost inverter circuit, specifically:

[0083] Given that the three-phase Buck-Boost inverter circuit is composed of three sets of Buck-Boost DC / DC converters with exactly the same structure, in the following analysis, phase A is taken as an example, and the other two phases are the same.

[0084] Figure 3The following is the equivalent circuit structure diagram of the A-phase Buck-Boost DC / DC converter provided by the present invention. For the two power switching tubes in the A-phase converter being in a complementary working state, their state differential equations are respectively established as follows:

[0085] State I: Q1 is on and Q2 is off:

[0086] (3);

[0087] State II: Q1 is off and Q2 is on:

[0088] (4);

[0089] In the formulas: is the system state vector, is the input-output state vector, i L is the inductor current, u C is the capacitor voltage, U in is the pulsed voltage on the input side of the converter, i o is the output current of the converter. A1, A2, B1, and B2 are all real-value matrices, specifically:

[0090] , ;

[0091] , .

[0092] Wherein: R on is the on-state equivalent resistance of the power switching tube, R L is the equivalent resistance of the inductor, and L and C are the inductor and capacitor values respectively.

[0093] Step (3): Establish an equivalent mathematical model between the input current and the input voltage of the three-phase uncontrolled rectifier circuit. The input current and the input voltage of the three-phase uncontrolled rectifier circuit are also the output current and the output voltage of the three-phase Buck-Boost inverter circuit. The equivalent mathematical model is specifically:

[0094] The three-phase uncontrolled rectifier circuit is equivalently composed of a dead zone module and a gain adjustment module, and its equivalent mathematical model is:

[0095] (5);

[0096] Wherein: i o and u o are respectively the output current and the output voltage of the three-phase Buck-Boost inverter circuit, where u o = U m sin ωt; u zis the limited value of the dead zone module, is the adjustment gain value, u z and The optimal values are obtained by numerical simulation method.

[0097] Step (4): According to the mathematical model obtained in step (1), the state differential equation obtained in step (2), and the equivalent mathematical model obtained in step (3), the discrete iterative mapping model of this DC regulated power supply is obtained, specifically:

[0098] From equations (1), (2), (3), (4) and (5), the discrete iterative mapping mathematical model of this DC regulated power supply is:

[0099] (6);

[0100] Where: i n+1 and u n+1 are respectively the inductor current and capacitor voltage of the converter at the (n + 1)T moment; T is the switching period of the power switch tube in the converter; α, β, e, X, Y are all intermediate variables, and are respectively: ; ; ; ; ; ; ; ; t a is the conduction time of the power switch tube Q1 in the (n + 1)th switching period T, t b is the turn-off time of the power switch tube Q1 in the (n + 1)th switching period T, i Lref is the inductor reference current, u Cref is the capacitor reference voltage, i n and u n are respectively the inductor current and capacitor voltage of the converter at the nT moment.

[0101] Step (5): In the range of the pulse voltage with variable amplitude and variable duty cycle corresponding to the PWM-modulated DC voltage, randomly select a set of pulse voltage amplitude and duty cycle, and according to the discrete iterative mapping model obtained in step (4), obtain the value range of the main circuit parameters for the stable operation of this DC regulated power supply through numerical simulation. The specific steps are:

[0102] Step (5-1): Set the system parameters, including: the equivalent resistance R L of the inductor L, the on-state equivalent resistance R on of the power switch tube, the switching period T, the maximum number of iterations K, the deviation value between adjacent two iterative variables, the capacitor reference voltage u Cref, the initial value of the iteration number n is taken as 1;

[0103] Step (5-2): Set the amplitude and duty cycle of the input pulse voltage to be U H and d0 respectively;

[0104] Step (5-3): Assume that the value of the main circuit inductor in the Buck-Boost converter remains unchanged, and take its value as L. Take the capacitor C in the Buck-Boost converter as the variable parameter, take its initial value as 0, and take ΔC as the variable step size;

[0105] Step (5-4): Calculate the inductor current i n+1 and capacitor voltage u n+1 at the (n + 1)T moment according to Equation (6);

[0106] Step (5-5): Judge whether both and are satisfied; if so, the system is in a stable state, execute Step (5-8), otherwise, execute Step (5-6);

[0107] Step (5-6): Judge whether the iteration number n is greater than K. If so, execute Step (5-7); otherwise, increase the iteration number n by 1 and return to Step (5-4);

[0108] Step (5-7): Add the set step size ΔC to the capacitor value C, reset the iteration number n to 1 and return to Step (5-4);

[0109] Step (5-8): Let the corresponding capacitor value at this time be the lower limit value C min of its stable region;

[0110] Step (5-9): Arbitrarily take a capacitor value C within the capacitor stable region determined in Step (5-8) and keep it unchanged. Take the inductor L as the variable parameter, take its initial value as 0, return the iteration number n to 1, and take ΔL as the variable step size;

[0111] Step (5-10): Calculate the inductor current i n+1 and capacitor voltage u n+1 at the (n + 1)T moment according to Equation (6);

[0112] Step (5-11): Judge whether both and are satisfied; if so, the system is in a stable state, execute Step (5-12), otherwise, execute Step (5-13);

[0113] Step (5-12): Add the set step size ΔL to the inductor value L, return the iteration number n to 1, and return to Step (5-10);

[0114] Step (5 - 13): Let the corresponding inductance value at this time be the upper limit value L of its stable region max ;

[0115] Step (6): Select n groups of pulse voltage amplitudes and duty cycles at certain intervals in sequence, and obtain the corresponding n - group value ranges of the main - circuit parameters according to the same method as in Step (5).

[0116] Step (7): According to the n - group value ranges of the main - circuit parameters obtained in Step (6) and their corresponding pulse voltage amplitudes and duty cycles, use the numerical fitting method to obtain the functional relationships between the value ranges of each main - circuit parameter and the pulse voltage amplitude and duty cycle; the numerical fitting method uses the multiple linear regression numerical fitting method; the functional relationships between the value ranges of each main - circuit parameter and the pulse voltage amplitude and duty cycle are as follows:

[0117] (1) The functional relationship of the lower - limit value of the capacitor is:

[0118] (7);

[0119] In the formula: U H is the high - level amplitude of the pulse input voltage, d0 is the duty cycle of the pulse input voltage, are all constant coefficients.

[0120] (2) The functional relationship of the upper - limit value of the inductor is:

[0121] (8);

[0122] In the formula: b0, b1, b2, b3, b4, b5 are constant coefficients.

[0123] In this embodiment, to verify the effect of the method for determining the stable region of the main - circuit parameters of the low - ripple adjustable DC regulated power supply based on the Buck - Boost inverter circuit provided by the present invention, the main technical parameters of this power supply are shown in Table 1.

[0124] Table 1 Main technical parameter table

[0125]

[0126] According to the discrete iterative mapping model obtained from Equation (6) and the technical parameters shown in Table 1, first taking the capacitor C as the variable parameter and keeping the inductor unchanged, use Matlab for numerical simulation to obtain the corresponding bifurcation diagram, as follows:

[0127] Set the high - level amplitude and duty cycle of the pulse voltage to be: U H = 400V, d0 = 0.5; Arbitrarily take the inductor L = 6×10 -6 H and keep it unchanged; Let the initial value of the capacitor C be 0, and take 5×10-8 F is the capacitance change step; numerical simulation is carried out according to the parameters set above, and the bifurcation diagram obtained is as Figure 4 shown. According to Figure 4 the bifurcation point capacitance value can be obtained as C = 3.10×10 -6 F. When the capacitance value C > 3.10×10 -6 F, the converter no longer exhibits bifurcation phenomena, that is, the system enters a stable operating state. This bifurcation point capacitance value is the lower limit value C min of its stable region.

[0128] Nine groups of pulse voltage amplitudes and duty cycles are selected at certain intervals, and the corresponding lower limit capacitance values C min for stable operation of the system are obtained by the same method as above, as shown in Table 2.

[0129] Table 2 Lower limit capacitance values C corresponding to different pulse voltage amplitudes and duty cycles min

[0130]

[0131] According to the nine groups of data obtained in Table 2, the function relationship between the lower limit capacitance value C min and the pulse voltage amplitude U H and the duty cycle d0 is obtained by using the multiple linear regression numerical fitting method, specifically:

[0132] (7);

[0133] In the formula: a0 = 2.06×10 -8 ; a1 = -2.67×10 -7 ; a2 = 1.13×10 -10 ; a3 = 4.7×10 -5 ; a4 = 1.86×10 -10 ; a5 = -1.92×10 -7 .

[0134] Similarly, any capacitance C = 1×10 -5 F is taken and kept constant within the capacitance stable region. Taking the inductance as the variable parameter, with its initial value being 0 and the inductance change step being 5×10 -8 H, and other technical parameters remaining unchanged, the bifurcation diagram obtained through numerical simulation is as Figure 5 shown. Similarly, according to the nine groups of pulse voltage amplitudes and duty cycles selected above, the corresponding upper limit inductance values L max for stable operation of the system are obtained by the same method as above, as shown in Table 3.

[0135] Table 3 Upper limit inductance values L corresponding to different pulse voltage amplitudes and duty cyclesmax

[0136]

[0137] Based on the 9 groups of data obtained from Table 3, the upper limit value of the inductance L is obtained by using the numerical fitting method of multiple linear regression max and the pulse voltage amplitude U H and the function relationship with the duty cycle d0 is specifically as follows:

[0138] (8);

[0139] In the formula: b0 = 4.30×10 -8 ; b1 = -3.67×10 -7 ; b2 = 2.11×10 -10 ; b3 = -5.27×10 -5 ; b4 = 1.70×10 -10 ; b5 = -8.87×10 -9 .

[0140] According to formulas (7) and (8), the corresponding fitting curves are respectively as Figure 6 、 7 shown.

[0141] To verify the effectiveness of the above function relationship, one set of main circuit parameters is randomly selected inside and outside the determined stable region of the main circuit parameters. For example, inside the stable region, the randomly selected main circuit parameters are: L = 8×10 -6 H, C = 1×10 -5 F, and outside the stable region, the randomly selected main circuit parameters are: L = 6×10 -6 H, C = 2×10 -6 F. Other main technical parameters are still as shown in Table 1. For the above two sets of main circuit parameters, simulation analysis is respectively carried out, and the corresponding output voltage waveforms are respectively as Figure 8 、 9 shown. It can be seen that for the main circuit parameters selected inside the stable region, the corresponding output voltage waveform is relatively smooth, indicating that the system is in a stable state; while for the main circuit parameters selected outside the stable region, the corresponding output voltage waveform has larger harmonics, indicating that the system generates oscillations and the system is in an unstable state. This further shows that the stable region of the main circuit parameters determined in this application is effective.

Claims

1. A method for determining the stability region of the main circuit parameters of a low-ripple adjustable DC regulated power supply based on a Buck-Boost inverter circuit, the main circuit of the DC regulated power supply includes a three-phase PWM rectifier circuit, a three-phase Buck-Boost inverter circuit and a three-phase uncontrolled rectifier circuit; characterized in that, The method for determining the stable region of the main circuit parameters includes the following steps: (1) Establish a mathematical model for the PWM-modulated DC voltage output by the three-phase PWM rectifier circuit; specifically: the three-phase PWM rectifier circuit adopts a space vector modulation strategy without zero vectors, and the obtained PWM-modulated DC voltage is a pulse voltage sequence with the pulse voltage amplitude and duty cycle varying with time. The mathematical model of the pulse voltage sequence is: The high and low level values of the i-th pulse voltage are: （1）； Where: U Hi is the high-level amplitude of the i-th (i = 1, 2, 3, …) pulse voltage, and U L is the low-level voltage value of the pulse voltage, V m and ω are the effective value and angular frequency of the input AC voltage of the three-phase PWM rectifier circuit respectively, t i and t i+1 are the starting moments of the i-th and the (i + 1)-th pulse voltages respectively, and t i ’ is the falling-edge moment of the i-th pulse voltage; The duty cycle of the i-th pulse voltage is: （2）； (2) Establish the state differential equation of the three-phase Buck-Boost inverter circuit; (3) Establish an equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit; (4) According to the mathematical model obtained in step (1), the state differential equation obtained in step (2), and the equivalent mathematical model obtained in step (3), obtain the discrete iterative mapping model of this DC regulated power supply; (5) Within the range of the pulse voltage with variable amplitude and variable duty cycle corresponding to the PWM-modulated DC voltage, arbitrarily select a set of pulse voltage amplitude and duty cycle, and according to the discrete iterative mapping model obtained in step (4), obtain the value range of the main circuit parameters when the DC regulated power supply operates stably under this set of pulse voltage amplitude and duty cycle through numerical simulation; (6) Change the pulse voltage amplitude and duty cycle in sequence at a certain interval, and obtain the value range of the main circuit parameters when the DC regulated power supply operates stably under this pulse voltage amplitude and duty cycle in n groups in the same way as in step (5); (7) According to the value range of the main circuit parameters obtained in step (6) in n groups when the DC regulated power supply operates stably under this pulse voltage amplitude and duty cycle and their corresponding pulse voltage amplitude and duty cycle, use the numerical fitting method to obtain the functional relationship between the value range of each main circuit parameter and the pulse voltage amplitude and duty cycle; (8) According to the functional relationship of the value range of each main circuit parameter obtained above and the pulse voltage amplitude and duty cycle on the input side of the Buck-Boost inverter circuit during the actual operation of the DC regulated power supply, obtain the value range of each main circuit parameter when the power supply operates stably under this pulse voltage amplitude and duty cycle.

2. The method for determining the stable region of the main circuit parameters of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit according to claim 1, characterized in that In step (2), when establishing the state differential equation of the three-phase Buck-Boost inverter circuit, specifically: Since the three-phase Buck-Boost inverter circuit is composed of three groups of Buck-Boost DC / DC converters with the same structure, in the following analysis, take phase A as an example, and the other two phases are the same; The two power switches Q1 and Q2 in the phase A converter are in a complementary working state. State differential equations are established respectively for its two complementary working states, which are: State I: Q1 is on, Q2 is off: （3）； State II: Q1 is off, Q2 is on: （4）； Where: is the system state vector, is the input-output state vector, i L is the inductor current, u C is the capacitor voltage, U in is the pulse voltage on the input side of the converter, i o is the output current of the converter. A1, A2, B1, and B2 are all real-valued matrices, specifically: ， ； ， ； Where: R on is the on-state equivalent resistance of the power switch transistor, and R L is the equivalent resistance of the inductor. L and C are the values of the inductor and capacitor respectively.

3. The method for determining the stable region of the main circuit parameters of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit according to claim 2, wherein In step (3), the specific steps for establishing the equivalent mathematical model between the input current and input voltage of the three-phase uncontrolled rectifier circuit are: The three-phase uncontrolled rectifier circuit is equivalently composed of a dead zone module and an adjustment gain module, and its equivalent mathematical model is: （5）； where: i o and u o are respectively the output current and output voltage of the three-phase Buck-Boost inverter circuit, where u o =U m sinωt; u z is the limit value of the dead zone module, a is the adjustment gain value, and the optimal values of u z and a are obtained by numerical simulation method.

4. The method for determining the stable region of the main circuit parameters of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit according to claim 3, characterized in that, In step (4), the specific steps for obtaining the discrete iterative mapping model are: The discrete iterative mapping mathematical model of this DC regulated power supply is obtained from Equations (1), (2), (3), (4) and (5) as follows: （6）； Where: i n+1 and u n+1 are respectively the inductor current and capacitor voltage of the converter at the (n + 1)T moment; T is the switching period of the power switch tube in the converter; α, β, e, X, Y are all intermediate variables, which are respectively: ; ; ; ; ; ; ; ; t a is the conduction time of the power switch tube Q1 within the (n + 1)th switching period T, t b is the turn-off time of the power switch tube Q1 within the (n + 1)th switching period T, i Lref is the inductor reference current, u Cref is the capacitor reference voltage, i n and u n are respectively the inductor current and capacitor voltage of the converter at the nT moment.

5. The method for determining the stable region of the main circuit parameters of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit according to claim 4, characterized in that, The specific steps of step (5) are as follows: Step (5-1): Set system parameters, including: equivalent resistance R of inductor L L , on-state equivalent resistance R of power switch tube on , switching period T, maximum number of iterations K, deviation value between variables of two adjacent iterations , capacitor reference voltage u Cref , initial value of iteration number n is taken as 1; Step (5-2): Set the input pulse voltage amplitude and duty cycle to U H and d0, respectively; Step (5-3): Assume that the value of the main circuit inductor in the Buck-Boost converter remains unchanged, and its value is taken as L. Taking the capacitor C in the Buck-Boost converter as the variable parameter, its initial value is taken as 0, and ΔC is taken as the variable step size; Step (5-4): Calculate the inductor current \(i\) at \((n + 1)T\) according to Equation (6) n+1 and the capacitor voltage \(u\) n+1 ; Step (5-5): Determine whether both and are satisfied; if so, the system is in a stable state and step (5-8) is executed; otherwise, step (5-6) is executed; Step (5-6): Determine whether the number of iterations n is greater than K. If so, execute step (5-7); otherwise, increment the number of iterations n by 1 and return to step (5-4); Step (5-7): Add the set step size ΔC to the capacitor value C, reset the number of iterations n to 1 and return to step (5-4); Step (5 - 8): Let the capacitance value corresponding at this time be the lower limit value C of its stable region min ; Step (5-9): Arbitrarily select a capacitor value C within the capacitor stability range determined in step (5-8) and keep it unchanged. Taking the inductor L as the variable parameter, its initial value is taken as 0, the number of iterations n is returned to 1, and ΔL is taken as the variable step size; Step (5 - 10): Calculate the inductor current \(i\) at \((n + 1)T\) according to Equation (6) n+1 and the capacitor voltage \(u\) n+1 ; Step (5-11): Determine whether both and are satisfied; if so, the system is in a stable state and step (5-12) is executed; otherwise, step (5-13) is executed; Step (5-12): Add the set step size ΔL to the inductor value L, return the number of iterations n to 1, and return to step (5-10); Step (5-13): Let the corresponding inductance value at this time be the upper limit value L of its stable region max .

6. The method for determining the stable domain of the main circuit parameters of the low-ripple adjustable DC regulated power supply based on the Buck-Boost inverter circuit according to claim 1, characterized in that The specific steps of step (7) are as follows: The functional relationship of the lower limit value of the capacitor is: （7）； Where: U H is the high-level amplitude of the pulse input voltage, and d0 is the duty cycle of the pulse input voltage, both are constant coefficients; The functional relationship of the upper limit value of the inductor is: （8）； Where: b0, b1, b2, b3, b4, b5 are constant coefficients.

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